Another type of temporally multiplexed SL system use N-ary gray-level patterns instead of binary patterns discussed above [1]}. This reduces the number of frames needed to achieve the same spatial resolution. Similarly, in communication systems, N-ary ECC is designed for N-ary symbol transmissions. As an example, Reed-Solomon code [2]} is one of the most commonly used N-ary ECC (e.g., in QR codes). However, the robustness of N-ary SL is not as high as binary SL. The N-ary pattern reduces the number of frames by \(\textrm {log}_2N\)  times. However, the interval between projector light intensity levels becomes \(N-1\)  times smaller. Therefore, given a fixed total exposure time and projector light intensity, the effective SNR reduces \(\frac{N-1}{\sqrt{\textrm {log}_2N}}\)  times when shot noise and ambient light dominates. This factor increases with bigger \(N\) . We compare the quantitative performance of the binary SL and N-ary SL systems, with or without ECC, in Fig. REF . We used 3-ary \((12,6,6)\)  Golay code and 8-ary \((7,3,6)\)  Reed-Solomon codes as examples, which has spatial resolutions 729 and 512. Accordingly, we use 10bits and 9bits binary patterns for comparison. Although N-ary ECC patterns indeed reduce the error rate compared with the uncoded N-ary patterns, their robustness are similar or worse than uncoded binary patterns with similar spatial resolution. Therefore, previously proposed self-correction methods based on N-ary gray-level SL [3]}, [4]} fail in this challenging situation.
